Elasticity of polymers investigated by atomic-force microscopy

The elasticity of four different polymers, polystyrene (PS), polypropylene (PP), polytetrafluoroethylene (PTFE) and linear low-density polyethylene (LLDPE), and a self-assembled monolayer (SAM) of 1H,1H,2H,2H-perfluorodecyltrichlorosilane (FDTS) on a silicon oxide substrate perforated with circular holes prepared by polymer blend lithography was investigated by atomic force microscopy (AFM) by using two different methods: a static and a dynamic method, under nondry-air conditions and at ambient temperature. In the static method based on the method developed by Oliver and Pharr for rigid indenters [J. Mater. Res. 1992, 7, 1564-1583], the elastic modulus is determined from load-displacement curves obtained from indentations of the cantilever tip in the sample surface. The origin of the observed plastic and elastic deformation phases is explained. As indentations performed by cantilever tips differ from those done by rigid indenters, parameters, such as creep of the piezoelectric scanner, cold flow, thermal expansion of the sample and finite stiffness of the cantilever were investigated to make the results fit the theoretical model of Oliver and Pharr. The method was tested on PTFE and PS. In the dynamic method based on the AFM method devised by Herruzo et al. [Nat. Commun. 2014, 5, 3126], a more robust measurement method than the initial one is used to determine the frequency shifts necessary to compute the elastic modulus of samples. This method, that is based on the tracking of the two first flexural contact resonances, is especially well suited when measuring in ambient conditions. The normal force necessary for the measurements was assessed. The origin of the observed plastic and elastic deformation phases and the effect of the spring constant on the relation between the measured normal force and the displacement of the Z piezoelectric scanner in these phases are explained.The method was tested on LLDPE, PP, PS and the SAM. The storage modulus of LLDPE, PP, PS and FDTS was determined. The values for LLDPE, PP, and PS where compared with Young's modulus for bulk material. The value of the storage modulus for FDTS can be used as an estimation for the order of magnitude of Young's modulus of an FDTS monolayer.The measurements were performed with two controllers for scanning probe microscopes (SPM): Nanonis, a commercial controller from Specs (Zurich, Switzerland), and SAPHYR, whose hardware was developed by the Electronics Department of the Department of Physics of the University of Basel (Basel, Switzerland) in collaboration with Nanosurf (Liestal, Switzerland), a company specialized in SPM. The full software for the control of the different modules of SAPHYR was programmed in the LabVIEW environment during this work. The functions necessary to perform elasticity measurements with Oliver and Pharr's methods, but also to perform AFM imaging in general, were implemented. These functions are a Z controller for the control of the tip-sample surface distance, a scanner that can map all the necessary quantities (phase shifts, frequency shifts, dissipation, ...) and a Z spectroscopy function that can measure load-displacement curves.The initial method for the computation of phase shifts between an excitation signal and the cantilever response signal with SAPHYR lockin amplifiers was replaced by a more powerful algorithm developed by the author.
In the initial method, the phase shift was determined from the real-time computation of ratio Y/X of the quadrature Y by the in-phase X components in the SAPHYR controller and the computation of arctan(Y/X) by the software for the control of SAPHYR. This algorithm, can compute arctan(Y/X) directly and precisely in the SAPHYR lockin amplifiers in real time. In addition, the algorithm overcomes the instabilities of the functioning of the initial phase-locked loops (PLLs) in SAPHYR based on the use of the approximation arctan(Y/X)~Y/X as a phase shift value, and due to magnitudes of phase shift and its variations greater than 0°, that occur, for example, when the cantilever tip picks up material or the sample surface elastic properties change. As this method is a good solution for the actual state of the art of the lockin and PLL development for AFM, my proposition for its patenting was accepted by the University of Basel. Finally, an analytical expression for the computation of the normal contact stiffness of a clamped cantilever with its tip in contact with the sample surface was established. This formula, derived from the equations based on Rabe's work and published by Hurley and Turner in J. Appl. Phys. 2007, 102, 033509, avoids the usual numerical determination of normal contact stiffness by the extrapolation method.